Coherent phonon dynamics of normal metal in ultrafast spectroscopy: Non-equilibrium gauge invariant Green's function approach

• Coherent phonon dynamics of normal metal in ultrafast spectroscopy is studied.
• Non-equilibrium phonon self-energy is found in terms of gauge invariant polarization functions.
• Polarization function is obtained by solving gauge invariant quantum Boltzmann equation.

The phonon dynamics of normal metal in the coherent regime of ultrafast spectroscopy is studied based on the non-equilibrium gauge invariant Green's function method. The non-equilibrium phonon self-energy is computed explicitly as a function of time in a gauge invariant way up to the second order of electric field of applied laser pulse. The extension beyond the coherent regime and the incorporation of correlation effects are discussed.